Comparison of two methods for the stochastic least cost design of water distribution systems

The problem of stochastic (i.e. robust) water distribution system (WDS) design is formulated and solved here as an optimization problem under uncertainty. The objective is to minimize total design costs subject to a target level of system robustness. System robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. The sources of uncertainty analysed here are future water consumption and pipe roughnesses. All uncertain model input variables are assumed to be independent random variables following some pre-specified probability density function (PDF). Two new methods are developed to solve the aforementioned problem. In the Integration method, the stochastic problem formulation is replaced by a deterministic one. After some simplifications, a fast numerical integration method is used to quantify the uncertainties. The optimization problem is solved using a standard genetic algorithm (GA). The Sampling method solves the stochastic optimization problem directly by using the newly developed robust chance constrained GA. In this approach, a small number of Latin Hypercube (LH) samples are used to evaluate each solution's fitness. The fitness values obtained this way are then averaged over the chromosome age. Both robust design methods are applied to a New York Tunnels rehabilitation case study. The results obtained lead to the following main conclusions: (i) neglecting demand uncertainty in WDS design may lead to serious under-design of such systems; (ii) both methods shown here are capable of identifying (near) optimal robust least cost designs achieving significant computational savings.